Question

10. What is the ratio of the interior angles of a
pentagon and a decagon?​

Answer 1

Given :-

A pentagon & A decagon .

To Find :-

• The ratio of the interior angles of a

pentagon and a decagon

CALCULATION :-

A pentagon has 5 sides.

Finding it's, interior angle sum,

Sum of the interior angles = ( n - 2) x 180

↗Sum of the interior angles = ( 5 - 2) x 180

↗ Sum of the interior angles = 3 x 180

➡ Sum of the interior angles = 540°

We, know sum of interior angle is interior angle / no. of sides of a polygon.

↗ int. angle = 540 ÷ 5

➡ So it's, interior angle = 108°.

Again interior angle of a decagon ,

n ( decagon) = 10 sides

Putting in, Sum of the interior angles = ( n - 2) x 180

↗Sum of the interior angles = ( 10 - 2) x 180

↗Sum of the interior angles = 8 x 180

➡ Sum of the interior angles = 1440°

Now , interior angle for the decagon.

↗ int. angle = 1440 ÷ 10

➡ So, the interior angles is = 144°

Now, the ratio of the interior angles,

↗ ratio of interior angle of pentagon : ratio of interior angle of decagon = 108 : 144

↗ 3 :4

▶ Hence, is the ratio of the interior angles of a

pentagon and a decagon is 3:4.

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